Polarization and Belief Convergence of Agents in Strongly-Connected Influence Graphs

TL;DR

This paper models how agents' beliefs evolve and polarize in strongly-connected influence networks, showing conditions under which polarization diminishes or persists, with implications for understanding opinion dynamics.

Contribution

It introduces a belief update model based on influence graphs and characterizes polarization convergence in strongly-connected, circulation, and clique graphs.

Findings

Polarization converges to zero in strongly-connected graphs.

In circulation graphs, agents reach a unique common belief.

Weakly-connected graphs may sustain polarization.

Abstract

We describe a model for polarization in multi-agent systems based on Esteban and Ray's classic measure of polarization from economics. Agents evolve by updating their beliefs (opinions) based on the beliefs of others and an underlying influence graph. We show that polarization eventually disappears (converges to zero) if the influence graph is strongly-connected. If the influence graph is a circulation we determine the unique belief value all agents converge to. For clique influence graphs we determine the time after which agents will reach a given difference of opinion. Our results imply that if polarization does not disappear then either there is a disconnected subgroup of agents or some agent influences others more than she is influenced. Finally, we show that polarization does not necessarily vanish in weakly-connected graphs, and illustrate the model with a series of case studies and simulations giving some insights about polarization.